Abstract
All the results we presented in the preceding two chapters are valid for hard spheres in the \(d \rightarrow \infty \) limit.
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Notes
- 1.
L is the side of the simulation cube.
References
R. Mari, J. Kurchan, Dynamical transition of glasses: from exact to approximate. J. Chem. Phys. 135, 124504 (2011). doi:10.1063/1.3626802
C. Rainone, The replica method in liquid theory: from the basics to explicit computations (2014), arXiv preprint arXiv:1411.3941
H.L. Frisch, J.K. Percus, High dimensionality as an organizing device for classical fluids. Phys. Rev. E 60, 2942–2948 (1999). doi:10.1103/PhysRevE.60.2942
F. Krzakala, L. Zdeborová, Hiding quiet solutions in random constraint satisfaction problems. Phys. Rev. Lett. 102, 238701 (2009). doi:10.1103/PhysRevLett.102.238701
G. Parisi, F. Zamponi, Mean-field theory of hard sphere glasses and jamming. Rev. Mod. Phys. 82, 789–845 (2010). doi:10.1103/RevModPhys.82.789
J. Kurchan, G. Parisi, F. Zamponi, Exact theory of dense amorphous hard spheres in high dimension. I. The free energy. JSTAT 2012, P10012 (2012)
P. Charbonneau et al., Numerical detection of the gardner transition in a mean-field glass former. Phys. Rev. E 92, 012316 (2015). doi:10.1103/PhysRevE.92.012316
M.S. Mariani, G. Parisi, C. Rainone, Calorimetric glass transition in a mean-field theory approach. Proc. Nat. Acad. Sci. 112, 2361–2366 (2015). doi:10.1073/pnas.1500125112
B. Lubachevsky, F. Stillinger, Geometric properties of random disk packings. J. Stat. Phys. 60, 561–583 (1990)
P. Charbonneau, Y. Jin, G. Parisi, F. Zamponi, Hopping and the Stokes-Einstein relation breakdown in simple glass formers. Proc. Nat. Acad. Sci. 111, 15025–15030 (2014)
A.T. Ogielski, Dynamics of three-dimensional Ising spin glasses in thermal equilibrium. Phys. Rev. B 32, 7384 (1985)
T. Aspelmeier, R.A. Blythe, A.J. Bray, M.A. Moore, Free-energy landscapes, dynamics, and the edge of chaos in mean-field models of spin glasses. Phys. Rev. B 74, 184411 (2006). doi:10.1103/PhysRevB.74.184411
G. Parisi, T. Rizzo, Critical dynamics in glassy systems. Phys. Rev. E 87, 012101 (2013). doi:10.1103/PhysRevE.87.012101
G. Parisi, The order parameter for spin glasses: a function on the interval 0–1. J. Phys. A: Math. Gen. 13, 1101 (1980)
P. Charbonneau et al., Fractal free energies in structural glasses. Nat. Commun. 5, 3725 (2014)
P. Charbonneau, Exact theory of dense amorphous hard spheres in high dimension. III. The full replica symmetry breaking solution. JSTAT 2014, P10009 (2014)
C. Rainone, P. Urbani, H. Yoshino, F. Zamponi, Following the evolution of hard sphere glasses in infinite dimensions under external perturbations: compression and shear strain. Phys. Rev. Lett. 114, 015701 (2015). doi:10.1103/PhysRevLett.114.015701
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Rainone, C. (2017). Numerics in the Mari-Kurchan Model . In: Metastable Glassy States Under External Perturbations . Springer Theses. Springer, Cham. https://doi.org/10.1007/978-3-319-60423-7_7
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